Megami Tensei

Megami Tensei ("Goddess Reincarnation"), know as Megaten for short, refers to both the 1987 NES game and the massive franchise that it spawned, though it should be noted that the whole franchise was really started by a novel series, Digital Devil Story (by Nishitani Aya), on which the game was based. Games falling under the Megaten umbrella to date include:

There are numerous ports as well that are not included in this list.
The series has also resulted in two animes: one movie also called Digital Devil Story and an anime series based on Devil Children.

The two defining points of the Megaten series are the ability to interact with 'demons', and the occult themes that tend to run through the games. It should be noted that in the Megaten universe, the word 'demon' applies to pretty much any mythological/religious entity. Everything from the seraph Michael to Vishnu to Baphomet is classed as a demon. And, if it's a demon, chances are you can try talking to it or summoning it into your party.